The role of data embedding in equivariant quantum convolutional neural networks

TL;DR

This paper explores how classical-to-quantum data embedding influences the performance of equivariant quantum convolutional neural networks (EQCNNs) in image classification, highlighting the importance of embedding choice for accuracy and generalization.

Contribution

It analyzes the impact of different data embeddings on EQCNN expressibility and classification accuracy, providing insights into embedding selection for geometric quantum machine learning.

Findings

Classification accuracy depends on the embedding method used.

Embedding choice affects the initial training performance.

The benefit of equivariance varies with dataset and embedding.

Abstract

Geometric deep learning refers to the scenario in which the symmetries of a dataset are used to constrain the parameter space of a neural network and thus, improve their trainability and generalization. Recently this idea has been incorporated into the field of quantum machine learning, which has given rise to equivariant quantum neural networks (EQNNs). In this work, we investigate the role of classical-to-quantum embedding on the performance of equivariant quantum convolutional neural networks (EQCNNs) for the classification of images. We discuss the connection between the data embedding method and the resulting representation of a symmetry group and analyze how changing representation affects the expressibility of an EQCNN. We numerically compare the classification accuracy of EQCNNs with three different basis-permuted amplitude embeddings to the one obtained from a non-equivariant quantum convolutional neural network (QCNN). Our results show a clear dependence of classification accuracy on the underlying embedding, especially for initial training iterations. The improvement in classification accuracy of EQCNN over non-equivariant QCNN may be present or absent depending on the particular embedding and dataset used. It is expected that the results of this work can be useful to the community for a better understanding of the importance of data embedding choice in the context of geometric quantum machine learning.